Zero-divisor graphs in commutative rings Page 1 Zero-divisor graphs in commutative rings
David F. Anderson, Michael C. Axtell, and Joe A. Stickles, Jr. Abstract This article surveys the …

In this book, we introduce several graphical representations of a ring. In the past three
decades, graphs constructed from algebraic structures have been studied extensively by …

In this paper we continue our study of annihilating-ideal graph of commutative rings, that
was introduced in (The annihilating-ideal graph of commutative rings I, to appear in J …

Let R be a commutative ring with identity. The zero-divisor graph of R denoted by Γ (R) is an
undirected graph Γ (R)=(V (Γ), E (Γ)), where V (Γ) is the set of non-zero zero-divisors of R …

Let R be a commutative ring with identity and M an R-module. In this paper, we associate a
graph to M, say Γ (M), such that when M= R, Γ (M) is exactly the classic zero-divisor graph …

Let M be an R-module. We associate an undirected graph Γ (M) to M in which nonzero
elements x and y of M are adjacent provided that xf (y)= 0 or yg (x)= 0 for some nonzero R …

Let G be a finite group. The intersection graph of subgroups of G is a graph whose vertices
are all non-trivial subgroups of G and in which two distinct vertices H and K are adjacent if …

In this article, explicit formulas for finding the determining number and the metric dimension
of the zero-divisor graph of Z_n and non-Boolean semisimple rings are given. In the case of …

Let S always denote a semigroup with zero. This paper is devoted to study some of
properties zero-divisor graph of S-act. We give several generalizations of the concept of zero …

Let R be a commutative ring with unity 1≠ 0 and let M be a unitary R− module. In this paper,
we derive some completeness conditions on the zero divisor graphs of modules over …